A331218 a(n) is the numbers of ways to write n = u + v where the decimal representations of u and of v have the same number of digits d for d = 0..9.

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 4, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 5, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 6, 1, 0, 1, 0, 1, 0, 1, 0, 1

Offset: 0

Author

Rémy Sigrist, Jan 12 2020

Keywords

• nonn
• base

Comments

In other words, a(n) is the number of ways to write n as the sum of two anagrams.

Leading zeros are ignored.

Examples

			For n = 44:
- we have the following ways to write 44 as a sum of two anagrams:
  u   v
  --  --
  13  31
  22  22
  31  13
- hence a(44) = 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..20000
• Rémy Sigrist, PARI program for A331218
• Rémy Sigrist, Scatterplot of (x, y) such that 0 <= x, y <= 10^3 and x and y are decimal anagrams (a(n) corresponds to the number of pixels (x, y) such that x+y = n)

Crossrefs

Cf. A330827 (ternary analog), A331216 (binary analog).

Programs

PARI

See Links section.